1. Field of the Invention
The invention relates to an arrangement for coding and decoding picture element signals (pels), obtained by line by line scanning of the picture elements of a picture, said picture element signals being transformed in a transformation arrangement for generating coefficient values. These coefficient values are quantized in a quantizing device and thereafter stored in a storage medium or transmitted to an associated receiver. For the recovery of the original picture element signals the quantized coefficients are applied to a retransformation arrangement which, as is also the transformation arrangement, is formed by a plurality of transformers T(i) of the order i, wherein i=1, 2, 3, . . . N and the transformer T(i) having i inputs and 2i outputs, the i inputs being connected to the i outputs of the preceding transformer T(i-1). Each transformer T(i) is formed by i auxiliary transformers each having an input connected to the associated output of the preceding transformer T(i-1); this auxiliary transformer also comprises an arithmetical unit having two inputs, one of which is connected directly and the other via a delay device to the input of the auxiliary transformer, the arithmetical unit having two outputs which represent two of the outputs of the transformer T(i).
2. Description of the Prior Art
For the storage or transmission of pictures it is advantageous to use the lowest possible number of information units and yet display the scanned picture as accurately as possible. Reducing the number of information units is possible if in a picture the redundancy and, possibly, also the irrelevance are significantly suppressed. It is known, for example from the periodical "IEEE Transactions on Computers", Vol. Com-19, No. 1, February 1971, pages 50 to 61 inclusive, or from the book by Pratt "Digital Image Processing", John Wiley and Sons, 1978, pages 232 to 278 inclusive, to use transformation coding to reduce the number of information units and to quantize the resultant coefficients. A non-linear characteristic is usually used for the quantization.
After the arithmetical operations are performed in the arithmetical unit, this unit produces an output quantity the value of which is located in a value range which is wider than the range in which the input quantity of the arithmetical unit (and consequently also of the auxiliary transformer) is located. This can be explained with reference to a Walsh-Hadamard-transformation of two picture element signals A and B. The transformation of these two picture element signals produces the two coefficients EQU F(1)=A+B EQU F(2)=A-B.
If now the two picture signals A and B had the maximum value, the coefficient F(1) would be of twice the value, that is to say a doubling of the value range has occurred. Depending on the polarity of A and B this also relates to the coefficient F(2). As the transformation arrangement is formed by a cascade arrangement of a plurality of transformers, doubling of the value range occurring in each transformer, the value range of the transformed signals is wider than the value range of the original picture signals.